Bibliographic Details
| Title: |
Convergent Interpolation to Cauchy Integrals over Analytic Arcs. |
| Authors: |
Baratchart, Laurent1 laurent.baratchart@sophia.inria.fr, Yattselev, Maxim1 myattsel@sophia.inria.fr |
| Source: |
Foundations of Computational Mathematics. Dec2009, Vol. 9 Issue 6, p675-715. 41p. 2 Graphs. |
| Subjects: |
Cauchy transform, Complex numbers, Interpolation, Differential equations, Asymptotic theory of algebraic ideals, Equilibrium |
| Abstract: |
We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth nonvanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes converge locally uniformly to the approximated Cauchy transform in the complement of the arc. This asymptotic behavior of Padé approximants is deduced from the analysis of underlying non-Hermitian orthogonal polynomials, for which we use classical properties of Hankel and Toeplitz operators on smooth curves. A construction of the appropriate interpolation schemes is explicit granted the parametrization of the arc. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
